A batch of industrial components contains 5 'Grade-A' units, 1 'Grade-B' unit, and 1 'Grade-C' unit. A quality control officer selects two units at random, one after the other, without replacement.
Construct a tree diagram to represent all possible outcomes of this selection process, including the probabilities for each branch.
Determine the probability that the officer selects exactly one Grade-B unit and exactly one Grade-C unit.
200 exam-style questions on OCR (MEI) A Level Maths 2.3 Probability, covering 2.3.1 Calculate the probability of an event, 2.3.2 Complementary events, 2.3.3 Expected frequency of an event, 2.3.4 Diagrams to calculate probabilities, 2.3.5 Mutually exclusive and independent events, 2.3.6 Add probabilities for mutually exclusive events, 2.3.7 Multiply probabilities for independent events, 2.3.8 Mutually exclusive and independent events (notation) (A-level only), 2.3.9 Venn diagrams for probabilities (A-level only), 2.3.10 Conditional probabilities (A-level only), and 2.3.11 Independence via conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.